অনুশীলনী ৫.২

অষ্টম শ্রেণি (মাধ্যমিক)- গণিত - বীজগণিতীয় ভগ্নাংশ - অনুশীলনী ৫.২ | NCTB BOOK

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(১৩)
গুণ কর :

(ক)
$\frac{9 x^{2} y^{2}}{7 y^{2} z^{2}}, \frac{5 b^{2} c^{2}}{3 z^{2} x^{2}}$ এবং $\frac{7 c^{2} a^{2}}{x^{2} y^{2}}$

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(খ)
$\frac{16 a^{2} b^{2}}{21 z^{2}}, \frac{28 z^{4}}{9 x^{3} y^{4}}$ এবং $\frac{3 y^{7} z}{10 x}$

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(গ)
$\frac{y z}{x^{2}}, \frac{z x}{y^{2}}$ এবং $\frac{x y}{z^{2}}$

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(ঘ)
$\frac{x - 1}{x + 1}, \frac{{(x - 1)}^{2}}{x^{2} + x}$ এবং $\frac{x^{2}}{x^{2} - 4 x + 5}$

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(ঙ)
$\frac{x^{4} - y^{4}}{x^{2} - 2 x y + y^{2}}, \frac{x - y}{x^{3} + y^{3}}$ এবং $\frac{x + y}{x^{3} + y^{3}}$

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(চ)
$\frac{1 - b^{2}}{1 + x}, \frac{1 - x^{2}}{b + b^{2}}$ এবং $(1 + \frac{1 - x}{x})$

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(ছ)
$\frac{x^{2} - 3 x + 2}{x^{2} - 4 x + 3}, \frac{x^{2} - 5 x + 6}{x^{2} - 7 x + 12}$ এবং $\frac{x^{2} - 16}{x^{2} - 9}$

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(জ)
$\frac{x^{3} + y^{3}}{a^{2} b + a b^{2} + b^{3}}, \frac{a^{3} - b^{3}}{x^{2} - x y + y^{2}}$ এবং $\frac{a b}{x + y}$

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(ঝ)
$\frac{x^{3} + y^{3} + 3 x y (x + y)}{{(a + b)}^{3}}, \frac{a^{3} + b^{3} + 3 a b (a + b)}{x^{2} - y^{2}}$ এবং $\frac{{(x - y)}^{2}}{{(x + y)}^{2}}$

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(১৪)
ভাগ কর : (১ম রাশিকে ২য় রাশি দ্বারা)

(ক)
$\frac{3 x^{2}}{2 a}, \frac{4 y^{2}}{15 z x}$

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(খ)
$\frac{9 a^{2} b^{2}}{4 c^{2}}, \frac{16 a^{3} b}{3 c^{3}}$

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(গ)
$\frac{21 a^{4} b^{4} c^{4}}{4 x^{3} y^{3} z^{3}}, \frac{7 a^{2} b^{2} c^{2}}{12 x y z}$

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(ঘ)
$\frac{x}{y}, \frac{x + y}{y}$

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(ঙ)
$\frac{{(a + b)}^{2}}{{(a - b)}^{2}}, \frac{a^{2} - b^{2}}{a + b}$

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(চ)
$\frac{x^{3} - y^{3}}{x + y}, \frac{x^{2} + x y + y^{2}}{x^{2} - y^{2}}$

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(ছ)
$\frac{a^{3} + b^{3}}{a - b}, \frac{a^{2} - a b + b^{2}}{a^{2} - b^{2}}$

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(জ)
$\frac{x^{2} - 7 x + 12}{x^{2} - 4}, \frac{x^{2} - 16}{x^{2} - 3 x + 2}$

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(ঝ)
$\frac{x^{2} - x - 30}{x^{2} - 36}, \frac{x^{2} + 13 x + 40}{x^{2} + x - 56}$

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(১৫)
সরল কর :

(ক)
$(\frac{1}{x} + \frac{1}{y}) \times (\frac{1}{y} - \frac{1}{x})$

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(খ)
$(\frac{1}{1 + x} + \frac{2 x}{1 - x^{2}}) (\frac{1}{x} - \frac{1}{x^{2}})$

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(গ)
$(1 - \frac{c}{a + b}) (\frac{a}{a + b + c} - \frac{a}{a + b - c})$

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(ঘ)
$(\frac{1}{1 + a} + \frac{a}{1 - a}) (\frac{1}{1 + a^{2}} - \frac{1}{1 + a + a^{2}})$

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(ঙ)
$(\frac{x}{2 x - y} + \frac{x}{2 x + y}) (4 + \frac{3 y^{2}}{x^{2} - y^{2}})$

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(চ)
$(\frac{2 x + y}{x + y} - 1) \div (1 - \frac{y}{x + y})$

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(ছ)
$(\frac{a}{a + b} + \frac{b}{a - b}) \div (\frac{a}{a - b} - \frac{b}{a + b})$

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(জ)
$(\frac{a^{2} + b^{2}}{2 a b} - 1) \div (\frac{a^{3} - b^{3}}{a - b} - 3 a b)$

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(ঝ)
$\frac{{(x + y)}^{2} - 4 x y}{{(a + b)}^{2} - 4 a b} \div \frac{x^{3} - y^{3} - 3 x y (x - y)}{a^{3} - b^{3} - 3 a b (a - b)}$

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(ঞ)
$(\frac{a}{b} + \frac{b}{a} + 1) \div (\frac{a^{2}}{b^{2}} + \frac{a}{b} + 1)$

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(১৬)
সরল কর।

(ক)
$\frac{x^{2} + 2 x - 15}{x^{2} + x - 12} \div \frac{x^{2} - 25}{x^{2} - x - 20} \times \frac{x - 2}{x^{2} - 5 x + 6}$

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(খ)
$(\frac{x}{x - y} - \frac{x}{x + y}) \div (\frac{y}{x - y} - \frac{y}{x + y}) + (\frac{x + y}{x - y} + \frac{x - y}{x + y}) \div (\frac{x + y}{x - y} - \frac{x - y}{x + y})$

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(গ)
$\frac{x^{2} + 2 x - 3}{x^{2} + x - 2} \div \frac{x^{2} + x - 6}{x^{2} - 4}$

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(ঘ)
$\frac{a^{4} - b^{4}}{a^{2} + b^{2} - 2 a b} \times \frac{{(a + b)}^{2} - 4 a b}{a^{3} - b^{3}} \div \frac{a + b}{a^{2} + a b + b^{2}}$

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$\frac{a^{4} - b^{4}}{a^{2} - 2 a b + b^{2}}, \frac{a - b}{a^{3} - b^{3}}, \frac{a + b}{a^{3} + b^{3}}$ তিনটি বীজগাণিতিক রাশি।

(ক)
১ম রাশিকে লঘিষ্ঠ আকারে প্রকাশ কর।

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(খ)
দেখাও যে, রাশি তিনটির গুণফল $\frac{a^{2} + b^{2}}{{(a^{2} - a b + b)}^{2}}$

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(গ)
১ম রাশিকে $\frac{a^{3} + a^{2} b + a b^{2} + b^{3}}{{(a + b)}^{2} - 4 a b}$ দ্বারা ভাগ করে ভাগফলের সাথে $\frac{a^{2}}{a + b}$ যোগ কর।

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(১৮)
$A = x^{2} - 5 x + 6, B = x^{2} - 7 x + 12, C = x^{2} - 9 x + 20$ তিনটি বীজগাণিতিক রাশি।

(ক)
$\frac{x}{y}$ এবং $\frac{x + y}{y}$ এর বিয়োগফল নির্ণয় কর।

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(খ)
$\frac{1}{B} + \frac{1}{C}$ কে লঘিষ্ঠ আকারে প্রকাশ কর।

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(গ)
$\frac{1}{A}, \frac{1}{B}, \frac{1}{c}$ কে সাধারণ হর বিশিষ্ট ভগ্নাংশে প্রকাশ কর।

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(১৯)
$A = x - 2, B = x^{2} + 2 x + 4, C = x^{3} - 8$

(ক)
যোগফল নির্ণয় কর : $\frac{a}{b c} + \frac{b}{c a} + \frac{c}{a b} + \frac{a - b}{a c}$

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(খ)
সরল কর : $\frac{1}{A} \times \frac{x - 2}{B} + \frac{6 x}{C}$

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(গ)
প্রমাণ কর যে, $\frac{1}{A} \times \frac{x - 2}{B} \div \frac{x + 2}{C} = 1$

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(২০)
$A = \frac{x^{2} + 3 x - 4}{x^{2} + 7 x + 12}, B = \frac{x^{2} + 2 x - 3}{x^{2} + 6 x - 7}, C = \frac{x^{2} + 12 x + 35}{x^{2} + 4 x - 5}$ তিনটি বীজগাণিতিক রাশি।

(ক)
A কে লঘিষ্ঠ আকারে প্রকাশ কর।

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(খ)
A+B কে সরল কর।

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(গ)
দেখাও যে, $B \times C \div \frac{x^{2} - 9}{x - 1} = \frac{1}{x - 3}$

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